Question

The odds against A solving a certain problem are 4 to 3, and the odds in favor of B solving the same problem are 7 to 5. What is the chance that the problem will be solved if they both try?

Answer 1

Hint: Probability of solved = P (5) = 1- now or then solves the problem. The chance that something will happen. How likely it is that some event will occur. Sometimes we can measure a probability with a number like "10% chance", or we can use words such as impossible, unlikely, possible, even chance, likely and certain.

Complete step-by-step answer:
Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
 Let the two events be EA and EB.
Odds against favor of A are 4: 3.
$ \Rightarrow $Odds in favor of A are 3: 4.
Probability of A for solving the problem = P (A) = 3/7
Probability that A does not solving the question
$P(\overline A ) = 1 - \dfrac{3}{7} = \dfrac{4}{7}$
Now, about B.
Odds in favor of B are 7: 5
Probability that B solves the problem = P (B) = 7/12
Probability that B does not solves the $P\left( {\overline B } \right) = 1 - \dfrac{7}{{12}} = \dfrac{5}{{12}}$ problem =
$P\left( {\overline B } \right) = 1 - \dfrac{7}{{12}} = \dfrac{5}{{12}}$
Probability that problem is solved = P (5) $ = 1 - \dfrac{4}{7} \times \dfrac{5}{{12}} = \dfrac{{64}}{{84}}$
P (5) = 1 – none of them solves the problem
$ = 1 - \dfrac{4}{7} \times \dfrac{5}{{12}} = \dfrac{{64}}{{84}}$
Therefore the answer is $\dfrac{{64}}{{84}}$ or $\dfrac{{16}}{{21}}$.

Note: In this type of question where probability is asked, solve one-by-one each event. Then summarise the question and solve accordingly. Probability is the level of possibility of something happening or being true. Possibility is a chance that something may happen or be true.